Is there a tool to remesh an object such that it contains a specified number of vertices?
Soooorrrttt oooff.  It will require some math on your part.  And it only works one direction (down, removing verts).  

You can tweak the Decimate modifier to collapse to a ratio of vertices kept.  If you know the number of vertices you want and the number you have is look-up-able, then you can directly calculate the ratio:

for target vertex count $t$, vertex count $v$, and ratio $r$ , it is simply
$t/v=r$ .

Remember, Blender can remove vertexes all day, but it can't add any.